Problem: Simplify; express your answer in exponential form. Assume $y\neq 0, q\neq 0$. $\dfrac{{(yq^{-5})^{3}}}{{(y^{2}q^{-1})^{2}}}$
Solution: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(yq^{-5})^{3} = (y)^{3}(q^{-5})^{3}}$ On the left, we have ${y}$ to the exponent ${3}$ . Now ${1 \times 3 = 3}$ , so ${(y)^{3} = y^{3}}$ Apply the ideas above to simplify the equation. $\dfrac{{(yq^{-5})^{3}}}{{(y^{2}q^{-1})^{2}}} = \dfrac{{y^{3}q^{-15}}}{{y^{4}q^{-2}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{3}q^{-15}}}{{y^{4}q^{-2}}} = \dfrac{{y^{3}}}{{y^{4}}} \cdot \dfrac{{q^{-15}}}{{q^{-2}}} = y^{{3} - {4}} \cdot q^{{-15} - {(-2)}} = y^{-1}q^{-13}$